Electromagnetism / Electrodynamics I · Boundary-value problems and uniqueness
Match one Fourier mode across an annular cylinder
Problem
In $a<s<b$, impose $V(a,\phi)=V_a\cos(2\phi)$ and $V(b,\phi)=V_b\cos(2\phi)$. Find $V(s,\phi)$ in the form $(As^2+B/s^2)\cos2\phi$ by solving for $A,B$. Verify both boundaries and state the regular solid-cylinder limit when $a\to0$ with bounded potential.
Hint
Multiply the boundary equations by $a^2$ and $b^2$ if useful.
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